The subject of the invention is the use of image processing to relax the opto-mechanical constraints or to simplify the combination of the objective or to increase the performance of the whole system or else to preserve the performance of the objective in difficult environments notably involving considerable changes in temperature. One of the aims of the invention is also to increase the depth of field in such a way as to improve 3D perception in the context, for example, of binocular driving applications with thermal vision.
The simplification lies, for example, in the removal of a focusing mechanism translating a group of lenses along the optical axis in order to compensate for pressure or temperature variations while keeping an image on the detector sharp. In conventional solutions, this mechanism is also used to switch from infinity sight to finite distance sight.
The invention uses a known principle: pupil encoding, which consists in inserting into an optical combination an optical filter which is generally a phase and/or amplitude plate, at the level of the pupil of the objective, making it possible to increase the depth of field. Image processing is used to carry out a deconvolution of the image by the signature of the objective with this plate making it possible to preserve a quality of the image in a given range of depths of field.
FIG. 1 represents an optical system comprising a focusing optic comprising one such filter. This optic comprises three lenses L1, L2 and L3, two traditional optical filters F1 and F2 performing for example the desired spectral transmission and the pupil encoding filter φ. As seen in FIG. 1, the filter is arranged in the vicinity of the pupil P, convergence point of the field rays in FIG. 1. It could also be arranged on the back surface of the lens L2 so as to decrease the optical interfaces.
The operating principle of the filter uses deconvolution via the impulse response of the optic or PSF, acronym of Point Spread Function. p is the response of the system to an infinitely small object. If we know the impulse response p of an optic, knowing an object f, the image f′ of f given by the optic has a value of:f′=fp                  being the symbol of the convolution,        In Fourier space, space of spatial frequencies, we have:        F′=F·P with F′, F and P Fourier transforms of f′, f and p        P is the modulation transfer function.        
To perfectly restore the object f, it would therefore be necessary, in this space, to invert F=F′/P. Unfortunately this operation is not always possible. It is even impossible when P goes through the origin and is numerically unstable when P is too low. When the optic is defocalized, the function P exhibits several zeros. It is therefore necessary to stabilize it to increase depth of field. Special phase filters are adapted for this task. Thus, this technique requires on the one hand a phase filter adapted to the function that one wishes to optimize, and on the other hand image processing that will make it possible to perform the deconvolution operation.
This technique has been the subject of various publications. The essential points tackled are the physical principles allowing the correction of geometric or dynamic aberrations or the correction of focusing defects and the technical principles for producing phase or amplitude correction filters. The targeted applications relate to the infrared field, microlithography and more generally the field of imaging.
The patents of the company CDM OPTICS filed by Edward Dowski relating to the physical principles are of particular relevance, and particularly patent applications WO/2004/090581, WO/2006/001785, and U.S. Pat. No. 6,069,738.
Others include the four articles by F. Diaz, F. Goudail, B. Loiseaux and J. P. Huignard respectively titled “Design of a complex filter for depth of focus extension”, Optics Letters 34, 1171-1173 (2009)—“Increase in depth of field taking into account deconvolution by optimization of pupil mask”, Optics Letters 34, 2970-2972 (2009)—“Comparison between a new holographically generated complex filter and the binary phase filter for depth of field extension”, SPIE, vol. 7329 (2009)—“Optimization of hybrid imaging systems including digital deconvolution in the presence of noise” in Imaging Systems, OSA technical Digest, paper IMD4 (2010).
In his thesis defended May 6, 2011 and titled “Système d'imagerie hybride par codage de pupille”, Frédéric Diaz describes a deconvolution algorithm using a Wiener filter. The relationship giving the distribution of light in the image I(x, y) involves the optic O(x, y), the PSF of the optic h(x, y), and the noise b(x, y). It is written, to the nearest magnification of the optic:I(x,y)=h(x,y)*O(x,y)+b(x,y)
In the absence of noise, the deconvolution filter is the inverse filter. In the spatial frequency space, we have:TF(d(σX,σY))=TF(h−1(σX,σY))
In practice, the noise must be taken into account and the Wiener filter is used, giving:
      TF    ⁡          (      d      )        =                    TF        ⁡                  (          h          )                    *                                                      TF            ⁡                          (              h              )                                                2            +                        S          B                          S          0                    *: transposed by a complex variable
And the estimate of the object has a value of:Ô(x,y)=d(x,y)*I(x,y),d(x, y) being the digital processing applied to the image.
SB and S0 are the spectral densities of the noise and of the object. This filter approaches the inverse filter when the noise is low and tends towards 0 when the signal is low. For optical systems whose aberrations vary in the field, it is possible to envisage multi-zone algorithms.
If we set a range of defocalization ψ in which we wish to correct the system by pupil encoding and image processing, the estimate of the object finally has a value of:Ôψ(x,y)=dψ(x,y)*I(x,y)or elseÔψ(x,y)=dψ(x,y)*hψ(x,y)*O(x,y)+dψ(x,y)*b(x,y)
Where dψ(x, y) and hψ(x, y) are respectively the digital processing assigned to the image and the impulse response of the optical system for the defocalization ψ. We then define a criterion EQMψ for the optimization by considering the root mean square deviation between the two quantities Ôψ and O. It has been demonstrated that the latter can be written:EQMψ=∫∫|TF[dψ(σX,σY)]·TF[hψ(σX,σY)]−1|2·S0(σX,σY)·dσX,σY+∫∫|TF[dψ(σX,σY)]|2·SB(σX,σY)·dσX,σY 
Of course, for a second range of defocalization ψ′, we obtain:EQMψ′=∫∫|TF[dψ′(σX,σY)]·TF[hψ′(σX,σY)]−1|2·S0(σX,σY)·dσX,σY+∫∫|TF[dψ′(σX,σY)]|2·SB(σX,σY)·dσX,σY 
The first term of the criterion EQMψ corresponds to the inequality between the PSF and the chosen filter, the second term is associated with the noise of the digital deconvolution. Thus, if the filter is optimized for the first defocalization ψ, then we have:∫∫|TF[dψ(σX,σY)]·TF[hψ(σX,σY)]−1|2=0and the difference between EQMψ and EQMψ′ has a value of:∫∫|TF[dψ(σX,σY)]·[TF[hψ′(σX,σY)]−TF[hψ′(σX,σY)]]|2·S0(σX,σY)·dσX·dσY 
Thus, the variation of the merit function is linked to the variations of the FTM of the optical system, including the phase filter, as a function of the defocalization. The quality of the optical chain for other defocalizations is therefore deduced from deviations in behavior since, if one does not know the defocalization a priori, the digital correction function dψ is set to a given value. For other values of defocalization, the filter is less well-adjusted.
Several types of filter are possible, the simplest being composed of a single phase shift, close to a phase difference having a value of π between two zones forming one of the surfaces of the filter. The ratio between the two surfaces is optimized for obtaining the best compromise between the signal-to-noise ratio noted S/B and the correction of the defocalizations for obtaining optimal geometric resolutions.
Other, more complex filters can be implemented and the geometries of the masks described in the literature of the prior art remain applicable to the correction of the defocalizations:                So-called cubic masks whose phase function φ(x, y) in an orthonormal coordinate frame (x, y) has a value of:φ(x,y)=α·(x3+y3);        The so-called CPP (Constant Profile Path) masks;        Masks whose phase function is a trigonometric function;        Simplified annular masks composed of concentric rings, each ring introducing a phase that is constant and different according to the ring. An example of such a filter containing only three rings is shown in FIG. 2. In this configuration, the central ring A1 has the same phase as the peripheral ring A3;        So-called polynomial masks, the filter being referenced in a coordinate frame (x, y), the variation of the phase of the phase filter is a polynomial in x and y. When the mask has radial symmetry, the variation of the phase of the phase filter is a polynomial in r, r representing the distance to the center of the filter;        Asymmetrical masks;        So-called semi-circular masks whose phase variation φ(x, y) of the phase filter verifies, the filter being referenced in a coordinate frame (x, y) in Cartesian coordinates or (r, θ) in polar notation:φ(x,y,r)=α·sign(x)·rβ or φ(x,y,r)=α·sign(n·θ)·rβ        for so-called semi-circular masks, α and β being constants and the function sign(x) having a value of 1 when x is positive and −1 when x is negative.        
The correction filter can also comprise an amplitude function, i.e. it comprises zones with variable optical transmission, beyond the phase function.
Dynamic filters also exist, i.e. filters whose phase or amplitude profile is electrically adjustable according to a chosen configuration. An example of one such filter is given in FIG. 3 which represents two partial cutaway views of a dynamic phase filter. On the left view, the filter is not addressed; therefore its phase is constant. On the right view, the filter is addressed.
This filter essentially comprises two layers, a first layer of BSO (Bismuth Silicon Oxide) and a second layer CL of smectic liquid crystals. These two layers are arranged between two layers of conductive transparent ITO (Indium Tin Oxide) one of which is connected to the electrical ground and the other to a constant voltage V0. The filter comprises a matrix of conductive electrodes with programmable voltages V. As can be seen on the right view in FIG. 3, by addressing the electrodes with different voltages V−, 0 and V+, the crystal molecules take different orientations, provoking various variations in optical index and therefore phase variations on the beams of light that cross the dynamic filter.
Certain versions of this liquid crystal filter can be addressed optically via an optically sensitive layer of BSO, using an auxiliary modulated light source.
As we have seen, whatever the type of correction introduced to the phase filter and whatever the image processing applied, it is necessarily limited to a given range of correction. In other words, if one wishes to use an optic over a large range of defocalizations, whether they are connected to variations in environment such as temperature or pressure or to the finite distance range of sight, the correction introduced by a phase filter can prove inadequate.